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Certain Hilbert spaces of entire functions
Authors:
D. J. Newman and H. S. Shapiro
Journal:
Bull. Amer. Math. Soc. 72 (1966), 971-977
MathSciNet review:
0205055
Full-text PDF
References |
Additional Information
- 1.
N.
Aronszajn, La théorie des noyaux reproduisants et ses
applications. I, Proc. Cambridge Philos. Soc. 39
(1943), 133–153 (French). MR 0008639
(5,38e)
- 2.
V.
Bargmann, On a Hilbert space of analytic functions and an
associated integral transform, Comm. Pure Appl. Math.
14 (1961), 187–214. MR 0157250
(28 #486)
- 3.
Leon
Ehrenpreis, Mean periodic functions. I. Varieties whose annihilator
ideals are principal, Amer. J. Math. 77 (1955),
293–328. MR 0070047
(16,1122d)
- 4.
E. Fischer, Über algebraische Modulsysteme und lineare homogene partielle Differentialgleichungen mit konstanten Koeffizienten, J. für Math. 140 (1911), 48-81.
- 5.
E. Fischer, Über die Differentiationsprozesse der Algebra, J. für Math. 148 (1917), 1-78.
- 6.
Leopold
Flatto, Donald
J. Newman, and Harold
S. Shapiro, The level curves of harmonic
functions, Trans. Amer. Math. Soc. 123 (1966), 425–436. MR 0197755
(33 #5918), http://dx.doi.org/10.1090/S0002-9947-1966-0197755-5
- 7.
E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Cambridge, 1931.
- 8.
J.
Horváth, Basic sets of polynomial solutions for
partial differential equations., Proc. Amer.
Math. Soc. 9
(1958), 569–575. MR 0103330
(21 #2104), http://dx.doi.org/10.1090/S0002-9939-1958-0103330-1
- 9.
Bernard
Malgrange, Existence et approximation des solutions des
équations aux dérivées partielles et des
équations de convolution, Ann. Inst. Fourier, Grenoble
6 (1955–1956), 271–355 (French). MR 0086990
(19,280a)
- 10.
Bernard
Malgrange, Sur une inégalité de F. Treves, Math.
Z. 72 (1959/1960), 184–186 (French). MR 0130569
(24 #A429)
- 11.
S.
N. Mergelyan, On completeness of systems of analytic
functions, Uspehi Matem. Nauk (N.S.) 8 (1953),
no. 4(56), 3–63 (Russian). MR 0058698
(15,411f)
- 12.
H.
Muggli, Differentialgleichungen unendlich hoher Ordnung,
Comment. Math. Helv. 14 (1942), 381–393. MR 0007194
(4,100d)
- 13.
D. J. Newman and H. S. Shapiro, A Hilbert space of entire functions related to the operational calculus, University of Michigan, Ann Arbor, 1964, 92 pp. (mimeographed notes).
- 14.
J.
F Treves, Lectures on linear partial differential equations with
constant coefficients, Notas de Matemátiea, No. 27, Instituto
de Matemática Pura e Aplicada do Conselho Nacional de Pesquisas, Rio
de Janeiro, 1961. MR 0155078
(27 #5020)
- 15.
Georges
Valiron, Sur les solutions des équations
différentielles linéaires d’ordre infini et à
coefficients constants, Ann. Sci. École Norm. Sup. (3)
46 (1929), 25–53 (French). MR
1509291
- 1.
- N. Aronszajn, La théorie des noyaux réproduisants et ses applications. I, Proc. Cambridge Philos. Soc. 39 (1943), 133-153. MR 8639
- 2.
- V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187-214. MR 157250
- 3.
- L. Ehrenpreis, Mean periodic functions. I, Amer. J. Math. 77 (1955), 293-328. MR 70047
- 4.
- E. Fischer, Über algebraische Modulsysteme und lineare homogene partielle Differentialgleichungen mit konstanten Koeffizienten, J. für Math. 140 (1911), 48-81.
- 5.
- E. Fischer, Über die Differentiationsprozesse der Algebra, J. für Math. 148 (1917), 1-78.
- 6.
- L. Flatto, D. J. Newman and H. S. Shapiro, The level curves of harmonic functions, Trans. Amer. Math. Soc. 123 (1966). MR 197755
- 7.
- E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Cambridge, 1931.
- 8.
- J. Horváth, Basic sets of polynomial solutions for partial differential equations, Proc. Amer. Math. Soc. 9 (1958), 569-575. MR 103330
- 9.
- B. Malgrange, Existence et approximation des solutilns des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier 6 (1955-1956), 271-355. MR 86990
- 10.
- B. Malgrange, Sur une inégalité de F. Trèves, Math. Z. 72 (1959), 184-188. MR 130569
- 11.
- S. N. Mergelyan, On the completeness of systems of analytic functions, Uspehi Mat. Nauk. 8 (1953), 3-63 (Russian). MR 58698
- 12.
- H. Muggli, Differentialgleichungen unendlich hoher Ordnung, Comment. Math. Helv. 14 (1942), 381-393. MR 7194
- 13.
- D. J. Newman and H. S. Shapiro, A Hilbert space of entire functions related to the operational calculus, University of Michigan, Ann Arbor, 1964, 92 pp. (mimeographed notes).
- 14.
- F. Trèves, Lectures on linear partial differential equations with constant coefficients, Rio de Janeiro, 1961, (mimeographed lecture notes). MR 155078
- 15.
- G. Valiron, Sur les solutions des équations differentielles linéaires d'ordre infini et à coefficients constants, Ann. Sci École Norm. Sup. (3) 46 (1929), 25-53. MR 1509291
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1966-11608-7
PII:
S 0002-9904(1966)11608-7
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